Oscillations and Waves
Beginner
Wave function
Source: High school physics (Chinese)
Problem Sets:
Waves
Problem
A wave propagates in the negative $y$ direction with amplitude $1.0\times10^{-2}$ m, frequency 550 Hz, and wave speed 330 m/s.
Write the equation of this wave.
$x = 1.0\times10^{-2}\sin\!\left(1100\pi t + \frac{10\pi}{3}y\right)$ m $\approx 1.0\times10^{-2}\sin(3.46\times10^{3}t + 10.5\,y)$ m.
The angular frequency, wavelength, and wave number are
$$\omega = 2\pi f = 2\pi(550) = 1100\pi \approx 3.46\times10^{3} \text{ rad/s},$$ $$\lambda = \frac{v}{f} = \frac{330}{550} = 0.60 \text{ m}, \qquad k = \frac{2\pi}{\lambda} = \frac{10\pi}{3} \approx 10.5 \text{ rad/m}.$$Because the wave travels in the $-y$ direction, the phase takes the form $(\omega t + ky)$:
$$x = 1.0\times10^{-2}\sin\!\left(1100\pi\, t + \frac{10\pi}{3}\,y\right) \text{ m}.$$